Design improvement of the conversion mechanism from balloon inflation to bending motion for inflatable film actuators

Various soft actuators have been investigated to overcome the drawbacks of conventional solid machines and explore the applications of soft robotics. In particular, and because they are expected to be applicable in minimally invasive medicine because of their safety, soft inflatable microactuators using an actuation conversion mechanism from balloon inflation to bending motion have been proposed for high-output bending motion. These microactuators could be applied to create an operation space by safely moving organs and tissues; however, the conversion efficiency could be further improved. This study aimed to improve conversion efficiency by investigating the design of the conversion mechanism. The contact conditions between the inflated balloon and conversion film were examined to improve the contact area for force transmission, with the contact area dependent on the length of the contact arc between the balloon and force conversion mechanism and on the amount of balloon deformation. In addition, surface contact friction between the balloon and film, which affects actuator performance, was also investigated. The generated force of the improved device is 1.21 N at 80 kPa when it bends 10 mm, which is 2.2 times the generated force of the previous design. This improved soft inflatable microactuator is expected to assist in performing operations in a limited space, such as in endoscopic or laparoscopic operations.


Introduction
Conventional robots constructed using hard materials have advantages in accuracy, stability, and modeling 1,2 . In recent years, soft robots have been explored to solve problems that are difficult for rigid systems and to broaden the possibilities of the robotics field [1][2][3][4][5][6][7][8][9][10][11] . Soft robots, constructed using soft and flexible materials, exhibit adaptive shape deformation when making contact with objects, making them inherently safer to use in situations where contact with humans and fragile objects occurs. As a result, soft surgical robots have been reviewed and discussed in terms of engineering design, fabrication techniques, and human-robot interactions 3 .
In previous studies, we developed soft actuators using pneumatic balloons, collectively named pneumatic balloon actuators (PBAs), and reported bending, torsion, and contraction motions [12][13][14][15][16][17] . The PBAs were fabricated using MEMS technology, including lithography, etching to form a casting mold, and molding of soft materials. Silicone rubber materials, such as polydimethylsiloxane (PDMS), are often used as soft and elastic materials. PBAs comprise two thin elastic films with different mechanical characteristics and utilize the asymmetrical deformation of these two elastic thin films for bending and twisting motions. In parallel, a conversion mechanism has been proposed for the highoutput bending and contracting motion of soft inflatable microactuators 14,16,17 . In these microactuators, the force conversion mechanism effectively converts the expansion force and displacement of the inflatable balloon into the desired motions with high force density. Figure 1a shows the appearance of the bending actuator with the conversion mechanism. As shown in Fig. 1c, the actuator consists of a PBA inserted between a force conversion film on the upper layer and Si-ribs on the lower layer. The force conversion film efficiently converts the balloon's expansion force into a bending force, and previous work has succeeded in significantly improving the generated force 16,17 .
According to numerous studies, the desired actuations have been realized using force conversion mechanisms at the microscale [18][19][20][21][22] . The actuator output, which decreases with miniaturization, has been converted and amplified by the force conversion mechanism to ensure its effective utilization in various actuations. The micro pneumatic gripper has been actuated by pressure, which has been converted into a reciprocating motion using piston bellows 18 . The flexural hinges, which have been found to convert the reciprocating motion into a grasping motion, have been fabricated by RIE and SU-8 UV-deep lithography and have been found to exhibit different properties depending on the material used. Microtweezers have converted the thin membrane expansion force due to applied pressure into a cantilever displacement for grasping motion 19 . In addition, the gripping force can be verified from the strain of the cantilever. The uniflex microactuator has been found to amplify tiny strains of the piezoelectric element, converting them into a large displacement 20 . Strain amplification has been realized by combining a unimorph with a strain amplification mechanism for flexural motion. An actuator that converted and amplified piezoelectric in-plane forces into out-of-plane forces and out-of-plane displacements has also been reported 21 . This actuator was developed by combining piezoelectric in-plane actuators and MEMSenabled scissor mechanisms. Two-axis actuators have converted in-plane motion into out-of-plane motion by utilizing the symmetry of the force conversion mechanisms 22 , with tilting motion utilizing the asymmetry of the force conversion mechanisms also reported.
In our previous work, we succeeded in increasing the output of this actuator by implementing the force conversion mechanism and achieved approximately 0.4 N (80 kPa) at a displacement of 10 mm (see Fig. 1a). Subsequently, by changing the material of the force conversion film from a polyimide film (PI) to a polyethylene terephthalate film (PET) and improving the bonding method, the adhesive properties were enhanced, with 0.55 N (force conversion film: PET, base film PI, 80 kPa) achieved under the same conditions. In the present work, we focused on the area of contact and attempted to further improve the force conversion efficiency. In this actuator, the balloon part expands when pressure is applied, and the force conversion film converts the expansion force into a bending motion. For this reason, as the contact area between the balloon and the force conversion film increases, the force conversion efficiency increases, and the generated force also increases. In this study, we further improved the generated forces using a high-efficiency design to increase the contact area between the balloon and the force conversion mechanism by means of a mechanical model.

Design
Driving principle of inflatable film actuator Figure 1a shows the appearance of the inflatable film actuator, and Fig. 1b shows the mechanical model of the driving principle for the actuator shown in Fig. 1a. The driving mechanism of the actuator is as follows: i. The balloon expands based on the applied pressure, and the force conversion film is lifted upward. The force vector received by the film at this point is defined as theF balloon .
ii. TheF balloon is decomposed by the force conversion film and transferred in the forward and backward directions relative to the balloon by the tensioning of the conversion film.
iii. The component of the transferred force that is vertical to the PBA and ribs is designatedF film . A moment of force is generated that depends onF film and the distance L from the center of rotation of the actuator flexion, and the actuator starts bending.
iv. The actuator bends until the moment of force generated by the balloon inflation is counterbalanced by an equal and opposite moment exerted by the load at its tip. The generated force can be changed by controlling the applied pressure.
As the momentM that contributes to the bending of the actuator increases, the generated force of the actuator also increases, andM is calculated by the following equation: AsF film increases in proportion toF balloon , the increase in the actuator moment depends on the three parameters, namely,F film ,F balloon , and L. Therefore, we can use a mathematical model to generalize the trend of these parameters.
Formulation of three parameters (F balloon,F film, L) Figure 2a shows a geometric model for formulating the three parameters. In the model, we consider the drive at a displacement of 10 mm. The geometric model was prepared to extract the parameters for higher output from the structural features of the device and to efficiently improve the design. It was prepared not for precise analysis but for efficient derivation of high-output design by combining the determined tendencies with simple experiments. For ease of modeling, we assumed that the balloon was hemispherical. Although the actual balloon was not hemispherical, the hemispherical balloon model can be used to derive designs effectively and experimentally for enhancing the output by extracting the necessary parameters from the model and determining the tendencies, which is the aim of this study.
First, we calculate the length of the vectorF front , |CE| (see Fig. 2a), to obtainF film . On the basis of trigonometry, since ∠DCE and ∠DCF are vertically opposite ∠OCG and ∠OCH, respectively, ∠DCE = ∠DCF = 90°− θ, we have ∠DCE = ∠CDE and ∠CED = 2θ because the quadrangle CEDF is a parallelogram. Focusing on △CDE, as shown in Fig. 2b, it is possible to obtain the following equation for |CE| using the law of sines: Then, we can calculate the length of the vectorF film .F front , which is transformed by the force conversion film and changes direction, is transmitted from position C-E to B-A through tension in the film.F film , a component of the pro-pagatedF front , is vertical to the OB. Thus,F film is calculated using the following equation: The same model is used to generalize for L. As shown in Fig. 2a, L is the length of OB, and it is calculated using the curvature radius of the balloon r as follows: From Eqs. (4) and (5), the momentM can be calculated using the following equation: The absolute value ofM is given by Eq. (6), and it approximately depends on r, θ, andF balloon . Figure 3 shows the mechanism ofF balloon generation. As shown in Fig. 3a, the same forceÑ is generated per unit contact area in the normal direction of the balloon surface when the balloon and film contact. The absolute value of N is calculated by the following equation:

Formulation ofF balloon
(P: applied pressure, dA: unit contact area) As shown in Eq. (7),Ñ is an infinitesimal surface element. From Fig. 3b, considering two pairs ofÑ forces that are symmetrical with respect to the line of force along which theF balloon acts, the resultant force acts in the upward direction. Focusing on a pair ofÑ forces that exist at an angle θ from the line of force along which theF balloon acts, the resultant forceF resultant generated by the twoÑ forces is calculated by the following equation: Additionally, Fig. 3a shows the frictional force between the balloon and the force conversion film. The frictional force depends onÑ in Eq. (7), the vertical drag due to the film's own weight, and the friction coefficient between the balloon and the film. The weight of the film, however, is negligible because it is sufficiently small compared to the expansion force of the balloon. The friction forcef per unit contact area dA between the balloon and the force conversion film is calculated as follows: (μ: Friction coefficient between the balloon and film.) As shown in Fig. 3a, the generated frictional force is vertical relative toÑ and acts in a direction that prevents balloon expansion in the tangential direction of the unit contact area. Figure 3c shows the downward resultant forcef resultant caused by a pair of forcesf existing at an angle θ from the line of force acted on by theF balloon . From Eqs. (8) and (9),f resultant is calculated as follows: Where values ofÑ generated at the position of angle θ from the line of force acted on byF balloon are numbered N 0 ,Ñ 1 ,Ñ 2 ,…,Ñ k (k = 0, 1, 2,…, k) starting from the balloon vertex, as shown in Fig. 3d, and the corresponding resultant forceF resultantðkÞ (k = 0, 1, 2,…, k) and the sum of these resultant forces,F upward , are also shown in Fig. 3d. The position k is the contact edge between the balloon and force conversion film. Figure 3e shows the friction forcef k (k = 0, 1, 2,…, k) generated at an angle θ from the line of force along which theF balloon acts, the corresponding resultant frictional forcef resultantðkÞ (k = 0, 1, 2,…, k), and the sum of these resultant forces F downward . Since the balloon expands isotropically,Ñ k is equal at every angle θ (all of number k), and the following equation is obtained:  Fig. 3 (See legend on next page.) Using Eq. (8),F resultantðkÞ can be obtained as follows: Similarly,f k (k = 0, 1, 2,…, k) and the corresponding resultant forcef resultantðkÞ are as follows: Within the forceF balloon exerted by the balloon on the force conversion film, the upward force that contributes to the generated force isF upward , and the downward force that reduces the generated force isF downward .F balloon is the sum ofF upward andF downward , andF upward andF downward are the sums ofF resultantðkÞ andf resultantðkÞ at each k (k = 0, 1, 2,…, k) position. Thus, the following equations hold:F balloon ¼F upward ÀF downward ð15Þ Figures 3d and 3e show thatÑ kÀ1 at position k−1 changes angle dθ until it reachesÑ k at position k. The following relationship can be obtained at this time using the infinitesimal angle dθ from Eqs. (11) and (12).
Then, to integrate Eqs. (18) and (19), we consider the force per unit contact areaÑ. Figure 3f shows the contact features of the balloon and the force conversion film. Since the balloon is spherical and the force conversion film is flat, they make contact along the arc that passes through the top of the balloon. The deformed balloon creates a contact area along the arc of contact. In Eq. (7),Ñ depends on the applied pressure P and the unit contact area dA. As shown in Fig. 3g, by approximating the width of the deformed part of the balloon as w and the balloon radius as r, dA is approximated as a rectangle with dimensions given by the arc length of the contact area rdθ and the deformed width of the contact area w. dA can be approximated by the following equation: Substituting Eq. (20) into Eq. (7) yields the following equation: The result of Eq. (21) is substituted into Eq. (18) for integration.
(see figure on previous page) Fig. 3 Mechanism of F ! balloon generation. a Force occurring between the balloon and the force conversion film: force vectorÑ in the normal direction of the balloon surface per unit contact area dA and friction force vectorf generated byÑ as a vertical drag force. b The force vectorF resultant from the composition ofÑ. c The force vectorf resultant generated by the composition off . dF upward , which is the sum of the resultant forceF resultantðkÞ at k = 0, 1, …, k arising fromÑ k (k = 0, 1,…, k) at each position. eF downward , which is the sum of thef resultantðkÞ at k = 0, 1, …, k resulting fromf k (k = 0, 1,…, k) generated at each position. f Characteristics of the contact between the balloon and force conversion film. The contact area occurs at the region of balloon deformation centered on the circular arc that passes through the balloon vertex. g The width w of the contact area around the circular arc is nearly constant and can be approximated. h Change inF balloon with increasing contact angle θ between the balloon and force conversion film:F balloon increases with decreasing friction coefficient µ, and the peak moves to the right (in the direction of increasing θ) The absolute value ofF upward is calculated as in Eq. (22), and from Eq. (19), the integral is similarly calculated.
Using the aforementioned results, we can calculate the net force in the upward direction, which is the force that is converted into the generated force.F balloon is the difference betweenF upward andF downward , so it is calculated from Eqs. (15), (22), and (23) as follows: On the basis of Eq. (24), it can be confirmed that the absolute value ofF balloon depends on the balloon radius r, contact angle θ, deformation width of the balloon w, and friction coefficient µ. Figure 3h  with appropriate values substituted. The vertical axis shows theF balloon , and the horizontal axis shows the angle θ between the line of force along which theF balloon acts and the edge of contact between the balloon and force conversion film. From Fig. 3h, the generated force increases with a lower friction coefficient µ, and the peak moves in the direction of increasing θ. Depending on the value of the friction coefficient, however,F balloon may decrease with increasing contact angle θ between the balloon and the force conversion film.

Consideration of balloon radius r and contact angle θ
From Eq. (6), the generated force of the actuator depends on the balloon radius r, the contact angle θ between the balloon and the force conversion film, andF balloon . From Eq. (24),F balloon depends on the balloon radius r, the contact angle θ, the deformation width of the balloon w, and the friction coefficient µ. In this section, the balloon radius r and contact angle θ are also considered. Figure 1a shows a side view of the driving actuator, and Fig. 4a shows a geometrical model based on this side view. The unbonded part forms a parallelogram when the actuator is driven, as shown in Fig.  4a. The arc length l of the contact area between the balloon and the force conversion film is calculated using the balloon radius r and the contact angle θ, as shown in the following equation: As shown in Fig. 3f, the contact area between the balloon and the force conversion film is generated at the region of balloon deformation around the circular arc. Therefore, a larger contact arc length l leads to an increasing number ofÑ, resulting in a largerF balloon . Figure 4a shows the geometric relationship that arises when the bonding position of the force conversion film is changed. It can be seen from the geometric relationship that θ is constant even when the bonding position is changed. The balloon radius, however, increases as the unbonded part of the force conversion film (Fig. 4a) decreases in length, and the contact circular arc l increases, as calculated in Eq. (25). From Eqs. (6), (24), and (25), it is expected that the actuator produces a higher generated force at a constant θ by increasing the balloon radius r, increasing the deformation width w, and decreasing the friction coefficient µ. Equations (6), (24), and (25) demonstrate that an increase in the balloon radius r has a significant effect on the generated force. In the following section, the effect of reducing the length of the unbonded part and changing the bonding position of the force conversion film on the generated force of the actuator is discussed.

Results and discussion
Characteristic evaluation of devices with a reduced length of the unbonded part Figure 4b-d shows the design of the device used in this experiment. The unbonded part length x of the force conversion film was set to 14, 16, 18, 20, and 22 mm, and the generated force at a device displacement of 10 mm was measured using a load cell. After each measurement, the bonding position of the force conversion film was changed, and measurements were repeated to compare the generated forces with the same device. The PI film was used as the force conversion film, and double-sided tape (NICETACK, NICHIBAN) and adhesive tape (vinyl tape, NICHIBAN) were used to attach the film for easy removal after measurement. As shown in Fig. 4c, d, we also measured the generated forces of the "forward-positioned device" and "backward-positioned device." These devices have an off-center unbonded part about the balloon, while the conventional devices have a center-positioned unbonded part about the balloon. Figure 4e shows the measurement results. The vertical axis is the generated force, and the horizontal axis is the length of the unbonded part. For all designs, the length of the unbonded part decreased, and the generated force tended to increase as the balloon radius r increased (from Eqs. (24) and (25)). The maximum generated force was observed for the backward-positioned device at x = 16 mm.
The following section describes the factors that led to the maximum generated force for the backward-positioned device and the subsequent reduction in the generated force at x = 14 mm. Figure 5a, b show the characteristics of the balloon deformation when the device is driven. The force conversion film lifts as the balloon expands, and the bending angle of the device increases when the tip of the device is unloaded (Fig. 5a). As shown in Fig. 5b, the bending angle of the device becomes constant when a load is applied to its tip, causing the force conversion film to stop moving. As a result, the balloon deforms along the film, while the contact area around the contact arc between the balloon and the force conversion film increases. The amount of deformation of the balloon along the force conversion film at this time determines the deformation width w in Eq. (24). In other words, with a smaller balloon expansion when the same load is applied to the tip of the device, the generated force of the designed device should be higher. Figure 5c, d show photographs of the forward-and backward-positioned devices, respectively, when the load was applied to the tip and the tension of the force conversion film began to increase. Figure 5c, d show that the balloon expansion of the backwardpositioned device was smaller than that of the forwardpositioned device. The smaller the unbonded region in front of the balloon was, the less the balloon expanded when the same load was applied to the device tip, and the wider the deformation of the balloon (denoted as width w) was.
Consequently, the generated force increased, and as a result, the generated force of the backward-positioned device was maximized, as shown in Fig. 4e. Figure 6a, b compare the contact between the sides of the balloon and the force conversion film for different unbonded parts. The contact angle θ rapidly increased when the balloon was pressed down by the force conversion film, causing it to make contact with the lower part of the balloon. As shown in Fig. 3h, there were cases in whichF balloon tended to decrease as the contact angle θ increased. The decrease in the generated force observed at x = 14 mm in Fig. 4e was attributed to the reduction inF balloon resulting from the effect of friction caused by the increased contact angle θ.
From the analysis described above, the optimal design for the friction coefficient µ of the currently used materials (PBA and force conversion film) was found to be close to the unbonded length x = 16 mm of the backward-positioned device. This was then confirmed experimentally.

Optimization of force conversion film bonding positions
In this experiment, we used PET film (with an improved bonding method) as the force conversion film of the device (Fig. 7b) and experimentally derived the optimal bonding position of the force conversion film. Figure 7a shows the relationship between the applied pressure and generated force for unbonded part lengths of x = 15, 16, and 17 mm (as shown in Fig. 4d) of the backwardpositioned device. The vertical and horizontal axes show the generated force and applied pressure, respectively, indicating the generated force at a 10 mm displacement. Based on Fig. 4e, the optimum design was considered to have an unbonded part length of approximately x = 16 mm, so the generated force at x = 16 ± 1 mm was measured. The range of applied pressure was 0 to 80 kPa The contact area increases when a load is applied at the device tip because the force conversion film is fixed and the balloon deforms along the film. c Expansion of the forward-positioned device: The balloon had to expand significantly before tension could be applied to the film in front of it. d Expansion of the backward-positioned device: The film in front of the balloon was tensioned even if the balloon expansion was small to accommodate the pressure endurance value of the balloon. For comparison, the generated force of the conventional device is also shown in Fig. 7a. The conventional device was the center-positioned device with x = 20 mm. As shown in Fig. 7a, the device with an unbonded part length of x = 16 mm had the largest generated force, which was 2.2 times (80 kPa) higher than that of the conventional device.

Effects of frictional force
As depicted in Fig. 4e, a decrease in the generated force was observed at an unbonded part length of x = 14 mm (center and backward-positioned). As x decreases, the contact angle θ increases, as shown in Fig. 6, and the generated force is expected to decrease, as shown in Fig.  3h (high µ). Figure 3h shows that a lower friction coefficient µ results in a higher generated force, and under this

Balloon
Force conversion film The side of the balloon contacts the force conversion film, and the contact angle ϑ increases rapidly.

Balloon Force conversion film
When the unbonded part is large Relationship between generated force and applied pressure. a The generated force of the device with unbonded part length x = 16 mm was~2.2 times higher than that of the conventional device (a center-positioned device with x = 20 mm). b In this experiment, we used PET film (with the improved bonding method) as the force conversion film condition, the maximum generated force was expected at x = 14 mm, where θ was the largest. Since the results in Fig. 3h were derived based on the center-positioned device model, the generated force characteristics of lower friction for the center-positioned device were examined to determine whether the tendencies of the force characteristics aligned with the theory, as shown in Fig. 3h. Figure 8 compares the generated force for centerpositioned devices with unbonded part lengths x = 14, 16, 18, 20, and 22 mm when the friction coefficient was reduced. Oil was applied to decrease the friction coefficient, and the generated force was measured under the same conditions used in the experiment, as shown in Fig.  4e. The friction coefficient of the oiled device was~0.1 and that of the non-oiled device was~1.2. As shown in Fig. 8, the generated force was larger for the oiled device with reduced friction, and it reached the largest at x = 14 mm, when the contact angle θ was at its maximum. These results were consistent with the determined tendencies presented in Fig. 3h.
On the basis of the aforementioned findings, we expect to achieve even higher outputs by using materials with lower friction coefficients to construct the actuator and by applying lubricants.

Conclusions
This paper presents the design of an inflatable bending actuator with a high force generation efficiency that uses a conversion mechanism based on a mechanical model. In this actuator, the balloon is expanded by applying pressure, and the force conversion mechanism converts the expansion force into a bending force to drive the actuator.
We focused on the contact area between the balloon and the force conversion film, which occurs at the deformed part of the balloon centered on the arc of contact, and we aimed to increase either the arc length of the contact arc (l) or the balloon deformation width (w). As a result, we proposed reducing the length of the unbonded part to achieve a high-output and efficient design. The results showed that the generated force initially increased as the length of the unbonded part decreased but subsequently decreased when the length of the unbonded part was further reduced. The generated force for the backward-positioned device was the largest. The results confirmed that for the friction coefficients of the currently used materials, the backward-positioned device was optimal, and, compared to that generated by the conventional design, this device successfully increased the generated force by~2.2 times. Oil was applied between the balloon and the force conversion film to confirm the effect of the friction force, and the generated force was evaluated. The results indicated that the tendencies observed in the theoretical models were consistent with the experimental results. Therefore, it is expected that additional increases in output could be achieved through further decreases in the friction coefficient.

Materials and methods
Fabrication process of the inflatable film actuator with bending motion Figure 1a shows the appearance of the inflatable film actuator, and Fig. 1c shows its structure. As shown in Fig. 1c, this actuator consists of a balloon structure (PBA) with a force conversion film on the surface and a 25-μm-thick polyimide film and 400-μm-thick Si-ribs on the back 16,17 . The PBA was fabricated using silicone rubber (KE-1606, Shin-Etsu Chemical Co., Ltd.). In our previous study, the force conversion film was made of polyimide film; however, in this study, a 25-μm-thick polyethylene terephthalate film (PET: Lumirror T60, Toray Industries, Inc.) and KE-1606 were used to improve the bonding performance. Since the force conversion film converts the expansion force of the balloon into a bending force, a superior bonding force with the PBA improves the force conversion efficiency between the expansion and bending forces. This is because by reducing the separation of the bonding surfaces, the tensile force of the force conversion film is transmitted to the acting part without decreasing. As a result, the generated force has improved.
PET films were bonded to KE-1606 thin films (KE-1606 was spin-coated at 2000 rpm on a Si wafer and thermally cured at 85°C for 10 min) using a silane coupling agent (3-mercaptopropyltrimethoxysilane) and irradiated with O 2 plasma. The PBA was then bonded to KE-1606, which was bonded to the PET film surface using surface activation (vacuum ultraviolet light). Experimental setup As shown in Fig. 1a, in this experiment, the generated force of the device at a displacement of 10 mm was measured for comparison with that of devices from previous works by combining a load cell (LVS-500GA, Kyowa Electronic Instruments Co., Ltd.) and a strain amplifier (DPM-911B, Kyowa Electronic Instruments Co., Ltd.). The device was fixed to a Z stage (TBM-603, SIGMA-KOKI), and the positioning of 10 mm displacement was controlled by a gauge equipped with the Z stage. The device was driven by applying pressure with a syringe pump (PUMP33, Harvard Apparatus). The pressure applied to the device was measured with a manometer (PG-100, Nidec). To reduce the frictional force, we applied a thin layer of silicone oil (KF-96-50CS, Shin-Etsu Chemical Co., Ltd.) between the force conversion film and the balloon in certain experiments. The friction coefficient was measured by contacting objects made of the same material as the force conversion film and balloon and then measuring the angle at which the object began to slide when tilted.